Diamonds have now lost four of six and face an uphill battle to finish in the top three places to qualify for Finals Day.
Storm, replying to 172-5 at Scarborough, were fired once more by Indian star Smriti Mandhana, with the 22-year-old continuing a sparkling run of form with 56 off 36 balls.
She shared an unbroken opening partnership of 101 inside 10 overs with New Zealander Rachel Priest (37).
Mandhana added to scores of 48, 37, 52 not out, 43 not out and 102 last time out against Lancashire Thunder.
Storm, seen home with four balls to spare by captain Heather Knight’s unbeaten 45 off 37, are level on 23 points with Loughborough Lightning at the top, albeit ahead on net run-rate.
Diamonds’ openers Beth Mooney and Lauren Winfield had shared 119 inside 14 overs, with Australian Mooney leading the way with 69 off 42 balls after the hosts won the toss.
Winfield added 48 at a fast scoring North Marine Road
Diamonds’ disappointed coach Paul Grayson said: “That was a missed trick, I think given the position we got into with the bat.
“We could have maybe got another 10-15 runs. I was really pleased with a lot of how we played. It was a good batting performance.
“Lauren has continued her good form, and it was nice to see Beth Mooney score some runs.
“At halfway I was very confident we could defend that score. I would much rather have been in our position than theirs, if I’m honest. But we know we were playing against a very good side, and things are going their way at the moment. The ball was chipped into gaps a few times. On another day they could have been taken.
“It’s frustrating to take because it’s a game we should have closed out.”
Diamonds will travel to Southampton to face their fellow strugglers Southern Vipers on Wednesday.